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Simplifying x4 + 12x3y + 35x2y2 = 0 Reorder the terms: 35x2y2 + 12x3y + x4 = 0 Solving 35x2y2 + 12x3y + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(35y2 + 12xy + x2) = 0 Factor a trinomial. x2((7y + x)(5y + x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(7y + x)' equal to zero and attempt to solve: Simplifying 7y + x = 0 Reorder the terms: x + 7y = 0 Solving x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 x + 0 = 0 + -7y x = 0 + -7y Remove the zero: x = -7y Simplifying x = -7ySubproblem 3
Set the factor '(5y + x)' equal to zero and attempt to solve: Simplifying 5y + x = 0 Reorder the terms: x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySolution
x = {0, -7y, -5y}
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